Gradient Filter Function

Question

I am trying to understand EXACTLY what the GradientFilter function in Mathematica is doing. As far as I can tell, it appears to be doing a convolution of a first derivative of a Gaussian with the user supplied data using some kind of padding on the edges because, I can replicate the results of the GradientFilter almost exactly by doing this except for the behavior at the edges due to the padding. However, one of my colleagues (a MATLAB user by the way) disagrees and thinks it is doing more than just that. Also, is there any way to see the convolution kernel that the GradientFilter is using given a certain radius and standard deviation? The documentation is somewhat ambiguous. So, if anyone out there has any insight to this, I would really appreciate it.